The generator matrix

 1  0  0  0  0  0  1  1
 0  1  0  0  0  0  X  0
 0  0  1  0  0  0  X  0
 0  0  0  1  0  0  X  0
 0  0  0  0  1  0  X  0
 0  0  0  0  0  1  X  0

generates a code of length 8 over Z2[X]/(X^2) who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+45x^2+12x^3+230x^4+220x^5+451x^6+792x^7+594x^8+792x^9+451x^10+220x^11+230x^12+12x^13+45x^14+1x^16

The gray image is a linear code over GF(2) with n=16, k=12 and d=2.
As d=2 is an upper bound for linear (16,12,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 12.
This code was found by Heurico 1.16 in 0.0126 seconds.